Talk:Data Coding Theory/Hamming Codes

move from "Algebra/Error Correcting Codes" to "Data Coding Theory/Hamming Codes"
It is my opinion that this module is out of place here in the algebra book, and that this material would better fit into the Communication Systems book (which already features some information about error-correction and digital coding). If nobody minds, I would like to perform the merger sometime soonish. --Whiteknight (talk) (projects) 12:37, 25 August 2006 (UTC)


 * I don't directly object, but it is important somehow when moving modules around like this to note that some topics are inter-discliplinary and it may be useful to try and write about some topics in several different ways. Discussion about error correcting codes from a mathmatical viewpoint might be written slightly different than how it would be discussed from a Communication Systems viewpoint.  One is highly theoretical and the other is more pragmatic on how can I use this right now.
 * That said, I don't see how this material is going to be used by people who are trying to learn Algebra, as this is some pretty advanced mathmatics that is involved here. I would expect this material more for something like a Descrete Mathmatics or Finite Mathmatics textbook intended for upper-division college students, not a freshman Algebra textbook.  --Rob Horning 15:01, 25 August 2006 (UTC)


 * Thanks for the quick reply on a page that seems "out of the way", at best. I agree with you that this module is highly-interdisciplinary, but I also must point out that the subject in this page has absolutely no business being in a book about "algebra", even if the hamming calculation does require the use of matrices (it also is going to require things like modulo-two arthmetic, which aren't well explained here). It also, on second though, might not belong in the Communication Systems book either (at least, not the way it is written now). I am working on creating a new book about Data Coding Theory, which would be a perfect home for this module, but i haven't had the time to implement it yet. Perhaps I will just keep an eye on this page, and merge it when I finally create the more appropriate book. --Whiteknight (talk) (projects) 18:29, 25 August 2006 (UTC)


 * Sounds fine to me. A good move.  --Rob Horning 16:03, 27 August 2006 (UTC)

Error in page
There is error in the page. Under section Hamming Code, bit a8 appears out of nowhere in b1 and b2:

"To detect single errors, it's also very simple. Suppose the codeword received is a1a2...a7, we compute 3 values

bo = a1 + a3 + a5 + a7 (mod 2) b1 = a2 + a3 + a7 + a8 (mod 2) b2 = a5 + a6 + a7 + a8 (mod 2)

then we declare the error is at the 22b2 + 2b1 + b0th position."

I have corrected it, and now it is OK.

Onno Bulk

Onnojb (discuss • contribs) 18:12, 3 March 2015 (UTC)


 * ✅. Thank you for fixing it, Onnojb. I confirm that the correct equations calculate b0 from every odd-numbered bit, b1 from odd-numbered pairs of bits, b2 from odd-numbered nybbles. --DavidCary (discuss • contribs) 17:17, 20 January 2016 (UTC)